Respondents to a Radio 4 poll put her ahead of her nearest rivals, Benjamin Zephaniah, Roger McGough and John Hegley. There has never been a woman Poet Laureate since the royal household created the position for John Dryden in 1668, although there is nothing in the rules to debar them.
"I don't think women are precluded from the laureateship," said Mark le Fanu of the Society of Authors, one of the bodies that will advise the prime minister about Ted Hughes's successor. "In fact I think Wendy's in with a strong chance because she shows you can be funny and accessible without any loss of quality."
The radio voters' choices reflect a preference for humorous and "performance" poetry, as well as for simplicity. Of the poets who had been discussed in the serious papers as candidates for the laureateship, Andrew Motion came 10th in the Front Row poll and James Fenton was unplaced. One other women - Ursula Fanthorpe - featured in the top 10.
Cope, 53, comes from Erith, in Kent, and lives in Winchester with the poet and critic Lachlan McKinnon. After graduating from St Hilda's College, Oxford, she taught at a London primary school for 15 years before her debut collection, Making Cocoa for Kingsley Amis, brought her instant fame in 1986.
The title poem was hardly more than an excuse for an attention-grabbing title, but the collection displayed all her sardonic wit, acidulous view of men, parodic skill and bittersweet melancholy.
Her second collection, Serious Concerns (1992), was full of big themes (love, death, parting, cricket) simply dealt with, often in nursery-rhyme metres, and smart urban jokes about drinking, cats and parking spaces. She also revealed a rare talent for writing about happiness, and a willingness to take on commissions - both of which would stand her in good stead for the laureate post, with its requirement that the holder should write commemorative verses for special Royal or national occasions.
Should Ms Cope not be appointed, the other women front-runners are:
t Carol Ann Duffy, OBE, 43 - Scots-born feminist, tough, direct, funny, combative and witheringly satirical. Author of Standing Female Nude, Selling Manhattan, The Other Country and Mean Time.
t Lavinia Greenlaw, 35 - uses science as a lens for inspecting the world and humanising our relationship with technology. Former poet in residence at the Science Museum.
t Elizabeth Jennings, CBE, 72. Oxford-educated Lincolnshire Catholic mystic. Her Sixties work (The Mind had Mountains, 1966) was full of mental breakdown and recovery. Later works feature religious themes and reflections on suffering.
t Jackie Kay, 37. Scottish performance poet famed for funny, ventriloquial monologues.
t Ruth Padel, 52. Former Oxford classics don and nightclub singer. "The sexiest voice in British poetry" (Independent on Sunday). Winner of last year's National Poetry Competition with "Icicles Round a Tree in Dumfriesshire".
t Jo Shapcott, 46. Arts administrator. Writes with wit and detachment about sexual politics, bodies, identity. New collection, My Life Asleep, is shortlisted for 1998 TS Eliot prize.Only poet to have won National Poetry Competition twice.
t Fleur Adcock, 64. New Zealand-born Londoner. Bejeweled exoticism combined with conversational plainness. Edited anthology of 20th century women's poetry.